In brief, neurons express several different membrane proteins. Some general examples (and not limited to these) are different ion channels, receptors for different neurotransmitters, docking proteins that enable the secretion of neurotransmitter(s), receptors for neurotrophic factors, and, depending on their developmental stage, receptors for guidance molecules. In addition, neurons are highly polarized, so that certain proteins are restricted to or enriched in certain parts of the cell. While some of these proteins might be found in other cell types, a certain type of neuron will have a certain complement of proteins that are characteristic of that neuronal type.
More details can be found in either a cell biology or neurobiology textbook. For more details on certain proteins, like ion channels, you can then look at books like "Ionic Channels of Excitable Membranes" by Bertil Hille. After you have the basics, you can then look at the current literature for you neurons of interest.
I think I did not fully describe my question. Firstly I am more interested in the neuronal membrane outer layer. As far as I understand (as a synthetic chemist) I should focus on lipids forming the bilayer, and I am especially interested in the polar part. I want to find something unique about this part of the cell.
Could you please give a reference on a book/paper to consult?
Unfortunately, I know very little about the lipids in the membrane, since it has been a very long time since I was studying the in vitro effects of long chain fatty acids and alcohols. There is a fairly large body of literature on the lipid rafts in the neuronal membrane. As for the actual lipids themselves, I think that you would be better off performing a PubMed search and looking for current reviews. Usually the Cell Biology textbooks do not specifically address neurons, and Neuroscience textbooks are more interested in the protein or carbohydrate components of the membrane.